I don't have a good On Topic Perl answer. :(

I haven't looked at the site thoroughly. The problem you might run into with Flash, is that it can be doing things more advanced than ordinary web pages. Many of the features are well beyond regular HTML.

My guess would be that you would be better off getting a good SWF decompiler and then studying the code. Maybe I am overlooking something, but I think it would be very difficult to extract all the various getURLs, loadVars, streaming multimedia and such with Perl. A SWF decomplier should make it obvious what is going on under the hood.

Once you sorted out the ActionScript, Perl could be a good way to download some or all of the content.